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Even Number

An Integer of the form $N=2n$, where $n$ is an Integer. The even numbers are therefore ..., $-4$, $-2$, 0, 2, 4, 6, 8, 10, ... (Sloane's A005843). Since the even numbers are integrally divisible by two, $N\equiv 0\ \left({{\rm mod\ } {2}}\right)$ for even $N$. An even number $N$ for which $N\equiv 2\ \left({{\rm mod\ } {4}}\right)$ is called a Singly Even Number, and an even number $N$ for which $N\equiv 0\ \left({{\rm mod\ } {4}}\right)$ is called a Doubly Even Number. An integer which is not even is called an Odd Number. The Generating Function of the even numbers is


See also Doubly Even Number, Even Function, Odd Number, Singly Even Number


Sloane, N. J. A. Sequence A005843/M0985 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein